Specify the default methods for MARS^{®}
Regression. The changes you make to the defaults remain until you change them again, even after
you exit Minitab Statistical Software.
Criterion for selecting optimal model
Choose between the following criteria to select the optimal number of basis
functions for the model. This selection does not affect the search for the basis
functions. If the 2 criteria select the same number of basis functions, then the
models from the 2 criteria are the same.
R-squared: Select this option to display results for the model with the maximum
R-squared value.
Mean absolute deviation: Select this option to display results for the model with the least
mean absolute deviation.
Predictor interactions
An interaction means that the effect of a predictor depends on the value of
other predictors. For example, the rate at which grain dries in an oven depends
on the time in the oven, but the effect of time depends on the temperature of
the oven. The time and temperature variables interact.
Order specifies the number of different predictors that can be in a basis
function. For example, an order of 2 indicates that the effect of a predictor
can depend on the value of 1 other predictor. An order of 3 indicates that the
effect of a predictor can depend on the value of 2 other predictors. An order of
4 indicates that the effect of a predictor can depend on the value of 3 other
predictors. The following basis functions are an example of an interaction of
order 3:
BF1 = max(0, X_{1} − 800)
BF2 = max(0, X_{2} − 50) * BF1
BF3 = max(0, X_{3} − 10) * BF 2
If you allow no interactions, the model uses the additive model. Predictors do
not interact in the additive model.
Maximum number of basis functions
The default value of 30 works well in most cases. Consider a larger value when
30 basis functions seems too small for the data. For example, consider a larger
value when you believe that more than 30 predictors are important.
If you are uncertain whether 30 is enough, review the initial results. For
example, a larger value is more likely to improve the fit of the model if the
R-squared value trends upwards as the analysis adds basis functions.
Minimum number of observations between knots
Allow MARS® to
choose
The analysis uses sample size and model complexity to automatically
select a value. The automatic value works well in most cases.
User
specified
A value of 1 indicates that consecutive data points are eligible to
be points where the basis function changes. The value of 1 allows
the most rapid changes in the model predictions. Use larger values
to create smoother models to explore more general relationships.
Such smoother models are sometimes less accurate over certain ranges
of the data.